Sensor system

ABSTRACT

A sensor system ( 10 ) for locating transmitters incorporates three vehicle-mounted patch antennas ( 30  to  34 ), a signal processing unit ( 40 ), a navigation unit ( 50 ) and a computer ( 60 ). The navigation unit ( 50 ) measures sensor system position using the Global Positioning System. The antennas ( 30  to  34 ) receive radiation from a transmitter ( 210 ) to be located and respond by generating output signals which are frequency downconverted and processing coherently by a digital signal processing unit ( 230 ). This produces elevation and azimuth phase data for the computer ( 60 ), which determines measured phase differences. The computer ( 60 ) also calculates expected phase differences from antenna positions and trial transmitter positions. It determines transmitter location from correlation between measured and expected phase differences. The position of a transmitter ( 210 ) is determined for a number of sensor system positions.

BACKGROUND OF THE INVENTION

1. Field of the Invention

This invention relates to a sensor system and a method for locatingtransmitters.

2. Discussion of Prior Art

It is known to locate transmitters with an antenna which is scanneduntil its signal is a maximum; this gives transmitter bearing relativeto the system but not intervening distance. The distance can bedetermined by two steerable directional antennas of known separation andrelative orientation: this gives two different transmitter bearings witha known baseline from which transmitter/system distance can becalculated. It suffers from the disadvantage of requiring two steerabledirectional antennas, which should ideally be spaced apart by a distancecomparable to that between the transmitter and location system. Ifspurious multipath signals are present, adequate accuracy may not beobtainable.

Pulse-echo target location systems (radar, sonar, lidar) are also wellknown. They employ directional antennas and determine target distancefrom pulse time of flight and direction from bearing of peak receivesignal. Features in the system field of view reflect interrogatingpulses irrespective of whether or not they are transmitters.

In applications such as surveillance, there is a requirement forlocating a transmitter to an accuracy of better than 5 m in a cubicspace of side 100 m. Current radars and direction finding systems eitherlack sufficient accuracy or are undesirably expensive and complex, andcan be difficult to mount on moving platforms of convenient size, egroad vehicles or aircraft.

U.S. Pat. No. 5,835,060 to Czarnecki et al discloses a long base lineinterferometer system for transmitter location. The system employsantennas at each end of the base line and measures phase differencesbetween antenna output signals at successive positions along a systemmovement path between 2 m and 100 m long. Discontinuities in phasemeasurement are removed by “unwrapping”, ie addition or subtraction of2π to produce phase values between π and −π. To remove an unwantedunknown phase constant, each successive measured phase difference issubtracted from the next along the measurement path to give a differenceof differences or differential. Differentials are also predicted, forgrid points being searched. Predicted differentials are then subtractedfrom measured equivalents to produce residuals; a cost function is thenderived which is the sum of the squares of the residuals reduced totheir principle value. The cost function with the lowest value is thestarting point for non-linear least squares convergence to obtain avalue for transmitter position, which can in turn be used as a newstarting point for a further iteration. Unfortunately, this technique issensitive to noise; moreover, as will be described later in more detail,simulation indicates that it is not sufficiently accurate, particularlyat low signal to noise ratios.

It is an object of the invention to provide an alternative form ofsensor system.

SUMMARY OF THE INVENTION

The present invention provides a sensor system for transmitter locationincorporating:

a) two receiver elements responsive to incident radiation by generationof respective signals,

b) a processing system for determining phase difference data for pairsof element signals,

c) means for measuring sensor system position in terms of position data;

d) computer apparatus for determining transmitter position from phasedifference data measured from processed element signals and calculatedfrom trial transmitter locations,

characterised in that the computer apparatus is arranged to locatetransmitters from magnitude or phase of circular functions ofdifferentials between measured and calculated phase difference data.

The invention provides the advantage that because circular functions areused it is not necessary to alter phase values by 2π or to calculateiteratively. Instead location is obtained directly. Moreover, simulationindicates that improved accuracy and noise immunity is obtained comparedto the prior art.

The processing system may be arranged to process a pair of elementsignals or a pair of frequency downconverted signals equivalent theretoby multiplying one signal of each pair in either case by a complexconjugate of the other to enable their phase difference to be measured.It may be arranged to determine phase difference by:

a) mixing each signal of a pair with sine and cosine reference signalsto determine in-phase and quadrature components,

b) multiplying each component of one signal by both components of theother to produce an in-phase component product, a quadrature componentproduct and two products of in-phase and quadrature components,

c) adding the in-phase component product to the quadrature componentproduct, and

d) subtracting one product of in-phase and quadrature components fromthe other.

The processing system may be arranged to digitise signals at a samplingrate prior to mixing with reference signals, the reference signals havea frequency of one quarter of the sampling rate, and mixing isimplemented by multiplication of alternate samples by and one othersample in four by −1.

The circular functions of differentials between measured and calculatedphase difference data may be complex exponents, and the computerapparatus may be arranged to determine actual transmitter location bysumming exponents over a range of system positions and to indicatetransmitter location from the magnitude or phase of this summation. Thecomputer apparatus may alternatively be arranged to determine actualtransmitter location by producing summations of the exponents over arange of system positions, to multiply the summations together to form aproduct and to indicate transmitter location as that corresponding to apredetermined magnitude or phase of this product.

The measuring means may comprise a GPS base station and co-located withthe receiver elements a GPS subsidiary station for co-operation with thebase station and provision of position data.

The sensor system may be movable relative to a transmitter to belocated, the base and subsidiary GPS stations being arranged to provideposition data and the computer apparatus being arranged to subtractcalculated phase differences from those of processed element signals fora series of sensor system positions.

The measuring means may be arranged to implement inertial navigation.

The system of the invention may incorporate at least three receiverelements disposed to define a plurality of measurement dimensions inwhich to locate a transmitter, and the receiver elements may be patchantennas.

In an alternative aspect, the present invention provides a method oflocating a transmitter having the steps of:

a) providing two receiver elements responsive to incident radiation bygeneration of respective signals,

b) determining phase difference data for pairs of element signals,

c) measuring sensor system position in terms of position data;

d) determining transmitter position from phase difference data measuredfrom processed element signals and calculated from trial transmitterlocations,

characterised in that transmitter position is determined from magnitudeor phase of at least one circular function of a differential betweenmeasured and calculated phase difference data.

Phase difference data may be determined for pairs of element signals bymultiplying one signal of each pair in either case by a complexconjugate of the other to enable their phase difference to be measured:this may be implemented by:

a) mixing each signal of a pair with sine and cosine reference signalsto determine in-phase and quadrature components,

b) multiplying each component of one signal by both components of theother to produce an in-phase component product, a quadrature componentproduct and two products of in-phase and quadrature components,

c) adding the in-phase component product to the quadrature componentproduct, and

d) subtracting one product of in-phase and quadrature components fromthe other.

Signals may be digitised during processing at a sampling rate prior tomixing with reference signals, the reference signals have a frequency ofone quarter of the sampling rate, and mixing is implemented bymultiplication of alternate samples by 0 and one other sample in four by−1.

Phase differences may be calculated for a plurality of possibletransmitter locations and actual transmitter location determined fromcorrelation between calculated and measured phase differences.

The at least one circular function may be at least one complex exponent.It may be a plurality of complex exponents, actual transmitter locationbeing determined by producing a summation of exponents over a range ofsystem positions and transmitter location being that associated with apredetermined magnitude or phase of this summation. Actual transmitterlocation may alternatively by determined by producing a plurality ofsummations of exponents over a range of system positions andcorresponding to respective dimensions of transmitter location,multiplying the summations together to form a product and indicatingtransmitter location to be that corresponding to a predeterminedmagnitude or phase of this product.

Position data is provided by means of a GPS base station co-operatingwith a GPS subsidiary station co-located with the receiver elements.

The receiver elements may movable relative to a transmitter to belocated, position data may be provided by base and subsidiary GPSstations and calculated phase differences may be subtracted from thoseof processed element signals for a series of sensor system positions.

The method may employ at least three receiver elements in the form ofpatch antennas disposed to define a plurality of measurement dimensionsin which to locate a transmitter.

BRIEF DESCRIPTION OF THE DRAWINGS

In order that the invention might be more fully understood, embodimentsthereof will now be described, by way of example only, with reference toaccompanying drawing, in which:

FIG. 1 is a schematic side elevation of a sensor system of the inventioninstalled in a road vehicle; FIG. 2 shows antenna positions in FIG. 1;FIG. 3 is a plan view equivalent of FIG. 2; FIG. 4 illustrates thesystem of the invention communicating with a global positioning system(GPS) satellite and base station; FIG. 5 illustrates the system of theinvention detecting a remote transmitter; FIG. 6 is a phase processingcircuit two of which are incorporated in the system of the inventionshown in FIG. 5; FIG. 7 illustrates operation of the invention insearching a volume for a transmitter; FIG. 8 is a graphical illustrationof transmitter location probability; and FIG. 9 compares prior artlocation accuracy with that of the invention.

DETAILED DISCUSSION OF EMBODIMENTS

Referring to FIGS. 1, 2 and 3, a sensor system 10 of the invention isinstalled in an estate car road vehicle 20. It incorporates three patchantennas 30, 32 and 34 mounted externally on one side of the vehicle 20,a signal processing unit 40, a navigation unit 50 and a computer 60. Thenavigation unit 50 is a satellite-based global positioning system (GPS)transceiver with an associated antenna assembly 70 mounted on a ladderrack on the vehicle roof The computer 60 is mounted in a forwardposition within the vehicle 20, whereas the processing and navigationunits 40 and 50 are to its rear.

In operation, the navigation unit 50 provides the computer 60 with apositional reference for a point P_(o) at the intersection of threeCartesian axes 130, 140 and 150, of which the first two are horizontaland the last vertical.

The antennas 30 to 34 are mounted on the vehicle 20 at distances of1.121 m, 0.162 m, 1.082 m respectively from the plane of the first twoaxes 130 and 140. They are distant 1.383 m, 1.383 m and 2.128 mrespectively from the plane of the second and third axes 140 and 150,and 0.948 m, 0.571 m and 0.854 m respectively from the plane of thefirst and third axes 130 and 150. They provide two antenna pairs 30/32and 30/34, the antennas of each pair being spaced apart in a respectivedimension to be searched for a transmitter.

The antennas 30 to 34 have patch dimensions of 97 mm (height)×100 mm(width)×3 mm (thickness). They have voltage standing wave ratios (VSVWR)between 1.23:1 and 1.25:1, and a receiving bandwidth of 18 MHz for aVSWR not exceeding 3:1. Each antenna 30 to 34 has a gain response oftypically 6 dBi with a polar response characteristic having 70°-widegain lobes in both E and H planes: here dBi indicates dB relative to anisotropic dipole.

Referring now to FIG. 4, the system 10 is shown in communication with aglobal positioning system (GPS) base station 160 and a GPS satellite 161for determination of position and from which vehicle yaw was inferred.It is a better option to include in addition an inertial navigationsystem because it determines attitude (pitch, yaw and roll) as well asposition but it adds to expense. The antenna assembly 70 incorporates abacklink antenna 70 a and a GPS antenna 70 b communicating respectivelywith the GPS satellite 161 and a backlink antenna 162 b of the basestation, which also has a GPS antenna 162 a. Positions are determinedwith respect to Cartesian axes 172, the base station 160 and the vehicle20 being at (x1, y1, z1) and (x2, y2, z2) respectively.

In operation, the satellite 161 communicates with both the navigationunit 50 and the GPS base station 160, and the GPS base station 160communicates with the navigation unit 50 via antennas 162 b and 70 a.This arrangement is a differential GPS system of known kind whose modeof operation will not be described in detail.

Referring now to FIG. 5, the sensor system 10 is shown in more detailtogether with the GPS base station 160 and a transmitter 210 to belocated. The transmitter 210 has a 1 GHz output signal with +20 dBmpower. The processing unit 40 includes a receiver 220 connected to theantennas 30 to 34 and to a digital signal processor (DSP) 230, which isalso connected to the navigation unit 50. The DSP 230 and the navigationunit 50 are connected to the computer 60.

In operation, the antennas 30 to 34 receive signals from the transmitter210 and respond by supplying output signals to the processor 40 forprocessing and subsequent input to the computer 60. At the same time,the navigation unit 50 measures antenna positions relative to apositional reference provided by its GPS transceiver and the GPS basestation 160 in combination. It provides positional data to the computer60 at a rate of 1 sample every 3 seconds. The vehicle 20 moves relativeto the transmitter 210, and the system 10 detects signals from thetransmitter 210 at many locations, for example 3000 locations. Thecomputer 60 processes the output from the processing unit 40 and thepositional data from the navigation unit 50 to calculate the transmitterposition relative to the system 10 for output at R.

The GPS base station 160 and the navigation unit 50 together, provide apositional reference for the system 10. This allows the positions of theantennas 30, 32 and 34 to be established to an accuracy of 10 cm.Without the GPS base station 160, ie using only a GPS station on thevehicle 20, this positional accuracy would only be ˜30 m. It isdesirable to search a volume of 10⁶ m³ to an accuracy of ˜2 m or better:a 30 m uncertainty is not acceptable.

The receiver 220 incorporates three signal processing channels (notshown) of like construction and connected to respective antennas 30, 32and 34 by cables which are as nearly equal in length as possible toavoid affecting phase differences between antenna signals. Usingstandard superheterodyne techniques well known in radar andcommunications, each channel downconverts the 1 GHz signal from itsassociated antenna to generate a 5 kHz base-band signal. It uses twomixing stages and filters to achieve this, employing 978.6 MHz firstlocal oscillator (LO) and a 21.395 MHz second LO. This is conventionaltechnology and will not be described further. The need or otherwise forfrequency downconversion depends on the magnitude of the transmitterfrequency and the speed of processing circuitry: downconversion can beomitted if the former is sufficiently low and/or the latter sufficientlyhigh.

The three signal processing channels together provide three base-bandchannel output signals each with a centre frequency of 5 kHz; they arereferred to as Ch1, Ch2 and Ch3 and are associated with antennas 30, 32and 34 respectively. As will be described later in more detail, thesystem 10 determines the phase differences between the Ch1, Ch2 and Ch3output signals for a number of positions of the vehicle 20 relative tothe transmitter 210. Because the absolute position of the vehicle 20 isknown from its navigation unit 50, the absolute position of thetransmitter 210 can be determined as will be described later.

The DSP 230 receives as input signals the Ch1, Ch2 and Ch3 outputsignals and a 5 Hz GPS data trigger or timing signal from the navigationunit 50. It incorporates two like processing circuits each obtained byreconfiguring a commercially available signal processing circuit as willbe described. It calculates phase differences between these signals foruse in the computer 60 for azimuthal and elevation calculations oftransmitter position. It processes coherently in the sense that phasedifference information contained in the signals J1 and J2 is preservedand processed to become computer accessible for subsequentdetermination. It processes the Ch1, Ch2 and Ch3 signals to determinetheir in-phase and quadrature components in each case, and thenprocesses the components to determine phase difference and amplitudeproduct. This is carried out for signal pairs Ch1/Ch2 and Ch1/Ch3, Ch1being used twice.

FIG. 9 shows a circuit 500 of which there are two in the DSP 230. It isconfigured by programming a general-purpose circuit No ADSP 2181manufactured by Analogue Devices Inc. It comprises both analogue anddigital circuits and is controlled by a 20 MHz clock. It receives twoanalogue input signals J1 and J2, these being Ch1 and Ch2 for one of thetwo circuits and Ch1 and Ch3 for the other. The circuit 500 has twosignal channels indicated by suffixes a and b to reference numerals.Apart from an additional function of signal inversion in channel b, thechannels have like functions and like-referenced components except forsuffixes, which will be omitted when describing both channels. Aspreviously mentioned and as will be described in more detail later, thecircuit 500 processes the signals J1 and J2 coherently in that itpreserves their phase information relative to one another; it transformsthem in such a way that their phase difference can be isolated anddetermined directly. At 600 the signals J1 and J2 are amplified anddigitised at a sampling frequency of 48,000 samples per second (48 kHz)giving digital data streams D1 and D2; the latter are low-pass filteredat 604 to reduce noise (cut-off frequency 10 kHz) producing filtereddata streams E1 and E2 respectively. J1 and J2 have a relative phasedifference of ψ and can be expressed by: $\begin{matrix}{{J1} = {A_{1}\cos \quad \omega_{1}t}} & (1) \\{{J2} = {A_{2}{\cos \left( {{\omega_{1}t} + \phi} \right)}}} & (2)\end{matrix}$

Sine and cosine (ie in quadrature) reference signals 608 and 612 of 12kHz frequency are mixed with the filtered data streams E1 and E2 at 616and 618: this produces mixed data streams I1p and Q1p for E1 and I2p andQ2p for E2; here I and Q indicate in-phase and quadrature componentsinto which the streams E1 and E2 are decomposed by mixing. The referencesignals are synchronised with and one quarter the frequency of thedigital sampling frequency of 48 kHz mentioned above; in consequencethere are four samples per cycle of each reference signal, ie thesamples are separated by reference signal quarter cycles or π/2 phaseangles. Moreover, the reference phase values at four successive samplesare 0, π/2, π and 3π/2: the cosines for these are 1, 0, −1 and 0, andthe sines are 0, 1, 0 and −1. Mixing with reference signals 608 and 612therefore reduces to setting alternate samples to zero and inverting oneother sample in four. It reduces required computation significantly.Digital processing in this way is superior to analogue for the usualreasons of time invariance, alignment etc. It is expressed by:$\begin{matrix}\left. {{I1p} = {{A_{1}\cos \quad \omega_{1}t\quad \cos \quad \omega_{2}t} = {\frac{A_{1}}{2}\left( {{{\cos \left( {\omega_{1} + \omega_{2}} \right)}t} + {{\cos \left( {\omega_{1} - \omega_{2}} \right)}t}} \right)}}} \right) & (3) \\\left. {{Q1p} = {{A_{1}\cos \quad \omega_{1}t\quad \sin \quad \omega_{2}t} = {\frac{A_{1}}{2}\left( {{{\sin \left( {\omega_{1} + \omega_{2}} \right)}t} - {{\sin \left( {\omega_{1} - \omega_{2}} \right)}t}} \right)}}} \right) & (4) \\{{I2p} = {{A_{2}\cos \quad \left( {{\omega_{1}t}\quad + \phi} \right)\cos \quad \omega_{2}t} = {\frac{A_{2}}{2}\left( {{\cos \left( {{\left( {\omega_{1} + \omega_{2}} \right)t} + \phi} \right)} + {\cos \left( {{\left( {\omega_{1} - \omega_{2}} \right)t} + \phi} \right)}} \right)}}} & (5) \\{{Q2p} = {{A_{2}\cos \quad \left( {{\omega_{1}t}\quad + \phi} \right)\sin \quad \omega_{2}t} = {\frac{A_{2}}{2}\left( {{\sin \left( {{\left( {\omega_{1} + \omega_{2}} \right)t} + \phi} \right)} - {\sin \left( {{\left( {\omega_{1} - \omega_{2}} \right)t} + \phi} \right)}} \right)}}} & (6)\end{matrix}$

The four component streams I1p, Q1p, I2p and Q2p are high-pass filteredat 624 or 626 with a cut-off frequency of 17 kHz: this removes lowerfrequency components involving ω₁-ω₂, and produces filtered componentstreams I1, Q1, I2 and Q2 respectively: $\begin{matrix}{{I1} = {\frac{A_{1}}{2}{\cos \left( {\omega_{1} + \omega_{2}} \right)}t}} & (7) \\{{Q1} = {\frac{A_{1}}{2}{\sin \left( {\omega_{1} + \omega_{2}} \right)}t}} & (8) \\{{I2} = {\frac{A_{2}}{2}{\cos \left( {{\left( {\omega_{1} + \omega_{2}} \right)t} + \phi} \right)}}} & (9) \\{{Q2} = {\frac{A_{2}}{2}{\sin\left( {{\left( {\omega_{1} + \omega_{2}} \right)t} + \phi} \right)}}} & (10)\end{matrix}$

These filtered data streams are mixed in pairs I1/I2, Q1/I2, Q1/Q2 andI1/Q2 at 640 or 642 producing mixed data streams I1.I2, Q1.I2, Q1.Q2 andI1.Q2. $\begin{matrix}\begin{matrix}{{{I1}.{I2}} = \quad {\frac{A_{1}A_{2}}{4}{\cos \left( {\omega_{1} + \omega_{2}} \right)}t\quad {\cos \left( {{\left( {\omega_{1} + \omega_{2}} \right)t} + \phi} \right)}}} \\{= \quad {\frac{A_{1}A_{2}}{8}\left( {{\cos \left( {{2\left( {\omega_{1} + \omega_{2}} \right)t}\quad + \phi} \right)}\cos \quad \phi} \right)}}\end{matrix} & (11) \\\begin{matrix}{{{Q1}.{I2}} = \quad {\frac{A_{1}A_{2}}{4}{\sin \left( {\omega_{1} + \omega_{2}} \right)}t\quad {\cos \left( {{\left( {\omega_{1} + \omega_{2}} \right)t} + \phi} \right)}}} \\{= \quad {\frac{A_{1}A_{2}}{8}\left( {{\sin \left( {{2\left( {\omega_{1} + \omega_{2}} \right)t} + \phi} \right)} + {\sin \quad \phi}} \right)}}\end{matrix} & (12) \\\begin{matrix}{{{Q1}.{Q2}} = \quad {\frac{A_{1}A_{2}}{4}{\sin \left( {\omega_{1} + \omega_{2}} \right)}t\quad {\sin \left( {{\left( {\omega_{1} + \omega_{2}} \right)t} + \phi} \right)}}} \\{= \quad {\frac{A_{1}A_{2}}{8}\left( {{\cos \quad \omega} + {\cos \left( {{2\left( {\omega_{1} + \omega_{2}} \right)t} + \phi} \right)}} \right)}}\end{matrix} & (13) \\\begin{matrix}{{{I1}.{Q2}} = \quad {\frac{A_{1}A_{2}}{4}{\cos \left( {\omega_{1} + \omega_{2}} \right)}t\quad {\sin \left( {{\left( {\omega_{1} + \omega_{2}} \right)t} + \phi} \right)}}} \\{= \quad {\frac{A_{1}A_{2}}{8}\left( {{\sin \left( {{2\left( {\omega_{1} + \omega_{2}} \right)t} + \phi} \right)} - {\sin \quad \phi}} \right)}}\end{matrix} & (14)\end{matrix}$

The mixed data streams I1.I2 and Q1.Q2 are summed at 650 a producing asummed data stream (I1.I2+Q1.Q2), which is converted at 658 a into RS232format to become an output K1. Similarly, the other mixed data streamsQ1.I2 and I1.Q2 are summed at 650 a after inversion of the latter at654, ie effectively subtracting one from the other, and this produces asecond summed data stream (Q1.I2−I1.Q2) converted at 658 b into RS232format to become the output K2; ie: $\begin{matrix}\begin{matrix}{{K1} = \quad {{{I1}.{I2}} + {{Q1}.{Q2}}}} \\{= \quad {\frac{A_{1}A_{2}}{8}\left( {{\cos \left( {{2\left( {\omega_{1} + \omega_{2}} \right)t} + \phi} \right)} + {\cos \quad \phi} + {\cos \quad \phi} -} \right.}} \\\left. \quad {\cos \left( {{2\left( {\omega_{1} + \omega_{2}} \right)t} + \phi} \right)} \right) \\{= \quad \frac{A_{1}A_{2}\cos \quad \phi}{4}}\end{matrix} & (15) \\\begin{matrix}{{K2} = \quad {{{Q1}.{I2}} - {{I1}.{Q2}}}} \\{= \quad {\frac{A_{1}A_{2}}{8}\left( {{\sin \left( {{2\left( {\omega_{1} + \omega_{2}} \right)t} + \phi} \right)} + {\sin \quad \phi} - {\sin \left( {{2\left( {\omega_{1} + \omega_{2}} \right)t} + \phi} \right)} +} \right.}} \\\left. {\left. {{\left. {\left. \quad {\sin \quad \phi} \right)\omega_{2}} \right)t} + \phi} \right) + {\sin \quad \phi}} \right) \\{= \quad \frac{A_{1}A_{2}\sin \quad \phi}{4}}\end{matrix} & (16)\end{matrix}$

The operations of mixing at 640/642 and summing at 650 implementsmultiplication of the contents of channel a in FIG. 6 by the complexconjugate of channel b's contents, giving outputs from which, therequired phase difference can be obtained. This process corresponds tocoherent mixing or multiplication of a signal from one antenna 30 by thecomplex conjugate of a signal. from another, ie 32 or 34, the coherencebeing effectively encoded as a complex output of the multiplication.

As alternatives to the circuit 500 approach, fast Fourier transforms orHilbert transforms are possible options but would either be inefficientor. would produce non-perfect I/Q balance with phase offsets withtransmitter frequency drift. The circuit 50 produces the desired outputusing cheap, small, easily available components and lends itself to easeof calibration as will be described later. It also enables results to beobtained very rapidly.

Phasing signals K1 and K2 incorporating phase sample information areclocked from the circuit 500 to the computer 60 in response to itsinternal clock (not shown) controlling analogue to digital conversion at600. They are asynchronous with position data from the navigation system50 and need to be associated with an appropriate vehicle position atwhich their corresponding antenna output signals were obtained. To dothis a timing mark signal is fed from the GPS system to. the circuit 500for onward transmission to the computer 60 and marking the timing ofsuccessive K1/K2 values. An individual timing mark is synchronous to thetime a respective position calculation is made in the GPS unit. The GPSsystem gives position every 0.2 second: to improve this position/timeresolution, interpolation is used to associate K1/K2 values withappropriate vehicle positions intermediate successive GPS positionswhere necessary. K1/K2 timing in each case is compared with GPS positiontiming and K1/K2 position is adjusted reflect the occurrence of theformer between two of the latter. The computer 60 stores data inchronological order on disk for the whole of the vehicle path andsubsequently processes it to yield transmitter position as will bedescribed.

The computer 60 derives the phase difference ψ between the two signalsJ1 and J2 from the ratio of Equation (10) to Equation (9) and theproduct of their magnitude from the square root of the sum of thelatters' squares, ie: $\begin{matrix}{\phi = {{\tan^{- 1}\left( \frac{K2}{K1} \right)} = {\tan^{- 1}\left( \frac{\sin \quad \phi}{\cos \quad \phi} \right)}}} & (17) \\{M = {\sqrt{\left\lbrack {{K1}^{2} + {K2}^{2}} \right\rbrack} = {{\left( \frac{A_{1}A_{2}}{4} \right)\sqrt{\left( {{\sin^{2}\phi} + {\cos^{2}\phi}} \right)}} = \frac{A_{1}A_{2}}{4}}}} & (18)\end{matrix}$

The computer 60 calculates the phase difference ψ between signals Ch1and Ch2 for vertically separated antennas 30 and 32, and that betweensignals Ch1 and Ch3 for horizontally separated antennas 30 and 34: thesecorrespond respectively to transmitter elevation (z axis position) andazimuth (xy plane position) relative to the vehicle 20. The computer 60stores each successive system or vehicle position and two respectivephase measurements. It is not in fact essential to evaluate Equation(18) for M, it being possible to use the phase difference ψ only tolocate a transmitter as will be described later. Use of M in additioncan improve accuracy.

The navigation unit 50 and the GPS base station 160 operate together toprovide a GPS positional reference for the vehicle 20 with better than 1m absolute accuracy on the earth's surface, much superior to 30 maccuracy obtainable from GPS navigation satellites. The position of thebase station 160 is a fixed reference point and the transmitter 210 islocated relative to it.

Referring now to FIG. 7, the vehicle 20 is shown searching a cubicvolume 710 of side length 100 m and defined with reference to x, y and zCartesian axes 712, 714 and 716 respectively. The volume 710 consists of10⁶ cubic cells such as 720 a and 720 b each of side length 1 m. Topermit illustration, many cells are omitted and their positions areindicated by chain lines such as 722. Each cell is represented byC_(ijk), i, j and k having values 1 to 100 and indicating cell positionrelative to axes 712 to 716. The vehicle 20 passes along a path 730through a sequence of locations P1 to P4 at each of which measurementsare made, ie Pq with q=1 to 4.

To locate the transmitter 210 in the volume 710, as will be describedlater in more detail, the computer 60 calculates differentials betweenphase differences of received antenna signals Ch1 to Ch3 and expectedphase differences calculated for trial positions of a transmitter; anexpected phase difference in elevation for a hypothetical transmitterlocated in a cell C_(ijk) is represented by Δθ_(e,Pq,ijk), andΔθ_(a,Pq,ijk) is the equivalent in azimuth. The transmitter 210 has ahigh probability of being within a cell C_(ijk) if expected phasedifferences Δθ_(e,Pq,ijk) and Δθ_(a,Pq,ijk) repeatedly give a good matchto corresponding measured phase differences Δθ_(e,Pq) and Δθ_(a,Pq) atsuccessive vehicle positions P1 etc.

At each vehicle position, the computer 60 calculates a phase differencewhich would be expected for signals received at the system 10 from atransmitter in a cell C_(ijk) as follows. In FIG. 7, L1, L2 and L3 aredistances from a cell 720 b to respective antennas 30, 32 and 34, andhave integral and fractional wavelength parts given by: $\begin{matrix}{{L1} = {\left( {n_{1} + \delta_{1}} \right)\lambda}} & (19) \\{{L2} = {\left( {n_{2} + \delta_{2}} \right)\lambda}} & (20) \\{{L3} = {\left( {n_{3} + \delta_{3}} \right)\lambda}} & (21)\end{matrix}$

where λ is transmitter signal radiation wavelength, n₁ , n₂ and n₃ areintegers and δ₁, δ₂ and δ₃ are fractions.

Elevation phase difference Δθ_(e,Pq,ijk) is calculated by the computer60 by subtracting Equation (19) from Equation (20) to obtain pathdifference and multiplying by 2π/λ, $\begin{matrix}{{{ie}\text{:}\quad \Delta \quad \theta_{e,{Pq},{ijk}}} = {2{\pi \left( {\delta_{2} - \delta_{1}} \right)}}} & (22)\end{matrix}$

Azimuthal phase difference Δθ_(a) is calculated similarly from Equations(19) and (21), $\begin{matrix}{{{ie}\text{:}\quad \Delta \quad \theta_{a,{Pq},{ijk}}} = {2{\pi \left( {\delta_{3} - \delta_{1}} \right)}}} & (23)\end{matrix}$

The positions of the base station 160 and of the vehicle 20 relative toit are known, and the absolute positions of cells in the volume 710 areknown, so the computer 60 calculates L1, L2 and L3 by geometry and fromthem expected phase differences.

In exponential form, operations performed in the DSP 230 on the signalsCh1, Ch2, Ch3 are as follows: $\begin{matrix}{{{{Ch1}(t)} \cdot {{Ch2}^{*}(t)}} = {B_{1}B_{2}^{{j\Delta}\quad \theta_{e,{Pq}}}}} & (24) \\{{{{Ch1}(t)} \cdot {{Ch3}^{*}(t)}} = {B_{1}B_{3}^{{j\Delta}\quad \theta_{a,{Pq}}}}} & (25)\end{matrix}$

Where: $\begin{matrix}{{{Ch1}(t)} = {B_{1}^{{j\omega}\quad t}}} & (26) \\{{{Ch2}(t)} = {B_{2}^{j{({{\omega \quad t} + {\Delta \quad \theta_{e,{Pq}}}})}}}} & (27) \\{{{Ch3}(t)} = {B_{3}^{j{({{\omega \quad t} + {\Delta \quad \theta_{a,{Pq}}}})}}}} & (28)\end{matrix}$

B₁, B₂ and B3 are signal amplitude coefficients, * denotes a complexconjugate and other terms have their conventional meanings.Multiplication of Ch1 by the complex conjugate of Ch2 and Ch3 inEquations (29) and (30) respectively in the DSP 230 results in removalof the time dependent ω term leaving the measured elevation andazimuthal phase differences Δθ_(e,pq) and Δθ_(a,Pq) as required.

The navigation unit 50 provides the computer 60 with locations D_(P1)etc for successive positions P1, P2 etc. At each position, the computer60 records all relevant data, ie location D_(P0q), measured phasedifferences Δθ_(e,Pq) and Δθ_(a,Pq,) and expected phase differencesΔθ_(e,Pq,ijk) and Δθ_(a,Pq,ijk) calculated for all possible transmitterlocations in the search volume 710; after the system has completed itsmovement along the trajectory 730, the computer 60 analyses this data byinvestigating the degree of correlation between expected and measuredphase differences to find a best match indicating a cell containing atransmitter. In the expressions for Ch1(t).Ch2*(t) and Ch1(t).Ch3*(t)above, B₁B₂ and B₁B₃ (M in Equation (18)) are arbitrarily set to unityfor convenience; ie this amplitude information is not used in thepresent example to reduce computation, although it would improveaccuracy and would be used if this were required. The computer 60produces expressions e^(jΔθ) ^(_(e,Pq)) and e^(jΔθ) ^(_(a,Pq))representing signal products in complex number or circular function formbased on the measured phase differences Δθ_(e,Pq) and Δθ_(a,Pq) forlocations D_(P1) etc. It repeats this for expected phase differencesΔθ_(e,Pq,ijk) and Δθ_(a,Pq,ijk) to give expected signal products e^(jΔθ)^(_(e,Pq)) ^(,ijk) and e^(jΔθ) ^(_(a,Pq)) ^(ijk).

To correlate expected and measure phase difference, the computer 60generates elevation and azimuth match coefficients Ne_(Pq,ijk) andNa_(Pq,ijk) for each of the cells C_(ijk); the match coefficients areproduced in each case by multiplying together the two respective signalproducts obtained-from measured and expected phase differences, ie:$\begin{matrix}{{Ne}_{{Pq},{ijk}} = {{^{{j\Delta}\quad \theta_{e,{Pq}}}^{{{- j}\quad \Delta \quad \theta_{e,{Pq}}},{ijk}}} = ^{j{({{{\Delta \quad \theta_{e,{Pq}}} - {\Delta \quad \theta_{e,{Pq}}}},{ijk}})}}}} & (29) \\{{Na}_{{Pq},{ijk}} = {{^{{j\Delta}\quad \theta_{a,{Pq}}}^{{{- j}\quad \Delta \quad \theta_{a,{Pq}}},{ijk}}} = ^{j{({{{\Delta \quad \theta_{a,{Pq}}} - {\Delta \quad \theta_{a,{Pq}}}},{ijk}})}}}} & (30)\end{matrix}$

Unlike the prior art of U.S. Pat. No. 5,835,060, 2π discontinuities inphase angle do not give serious difficulty in Equations (29) and (30)because the exponents therein are circular functions: ie a small errorwhich alters a phase difference from nearly 2π to just above zeroremains a small error with only a small effect on the exponent.

In order to locate a transmitter, one could seek a maximum value ineither Ne_(Pq,ijk) or Na_(Pq,ijk) at a single system position providingdata for one elevation dimension or two azimuth dimensions respectively.However, greater accuracy is obtained by combining data: to implementthis, for each cell C_(ijk) , the elevation match coefficientsNe_(Pq,ijk) for all Q system positions (ie P1 to P4) are summed toprovide a trajectory elevation match coefficient Me_(ijk), and likewiseazimuth equivalents Na_(Pq,ijk) and Ma_(ijk), ie: $\begin{matrix}{{Me}_{ijk} = {\sum\limits_{q = 1}^{Q}\quad {Ne}_{{Pq},{ijk}}}} & (31) \\{{Ma}_{ijk} = {\sum\limits_{q = 1}^{Q}\quad {Na}_{{Pq},{ijk}}}} & (32)\end{matrix}$

Me_(ijk) and Ma_(ijk) each contain measured and expected transmitterphase histories in the form of exponents of differentials betweencorresponding phase differences. Here again one could seek a maximumvalue in either Me_(ijk) or Ma_(ijk) in order to locate a transmitter,but greater accuracy may be obtained by combining them: to implementthis, their moduli or magnitudes are multiplied together for each cellto give an overall match indicator V_(ijk), ie: $\begin{matrix}{V_{ijk} = {{{Me}_{ijk}}{{Ma}_{ijk}}}} & (33)\end{matrix}$

The transmitter position is within a cell C_(ijk) associated with amatch indicator V_(ijk) of greatest value. This is a single passdetermination: ie there is no necessity for the construction of V_(ijk)to be followed by iterative least squares fitting. V_(ijk) couldpossibly be constructed from the complex values of Me_(ijk) and Ma_(ijk)instead of their moduli, but the result may be undesirably sensitive tosmall errors in phase.

Me_(ijk) or Ma_(ijk) may be employed to calibrate the system 10. Each isa complex number, but should have a zero value of its imaginary part(zero phase) when its magnitude is a maximum: this is because theNe_(Pq,ijk) and Na_(Pq,ijk) values they contain will all have zeroexponents; ie measured and expected phase differences will be equal andtheir differentials zero ignoring noise and minor inaccuracy intransmitter position off-centre of a cell. If Me_(ijk) or Ma_(ijk) doesnot in fact have zero phase at maximum magnitude, it indicates that thesystem 10 has introduced a phase error due to unequal antenna cablelengths, unmatched receiver chains etc: if so the phase difference errorat the maximum of one of these quantities may be measured and removed,from later phase measurements by the computer in a calibrationoperation. Such a calibration is likely to remain valid for asubstantial length of time, because each pair of antennas and associatedprocessing circuitry are in the same environment: any drift is likely tobe common to both antennas and therefore to cancel out.

It is possible to modify the approach illustrated in FIG. 7 usingmultiple values of resolution, ie firstly a coarse resolution search tolocalise. the transmitter to a region of a few cells or a large cell ofsay 3 m side length, followed by one or more finer resolution searchesto increase accuracy. This reduces the number of computer calculationsrequired. It is also possible to use super resolution as described inU.S. Pat. No. 4,963,877 to resolve multiple sources of signals which aretoo close together to be resolved according to the Rayleigh criterion.

The system 10 evaluates all possible target positions within a searchvolume to a prearranged resolution by comparing the phase history ofreceived antenna signals with an expected transmitter phase historyobtained by calculation. This reduces the possibility of false alarmsbecause a whole environment is assessed. Multiple targets if any maybecome apparent, if necessary using super resolution as aforesaid. Anautomated search may be used.

Referring now to FIG. 8, there is shown a two-dimensional plot 800 ofthe variation in trajectory azimuth match coefficient Ma_(ijk) referredto above, ie transmitter location indicator in azimuth over one layer ofcells (cells having the same value of j index or y axis position anddifferent values for ik index pairs). Graphs 810 and 820 indicatevariation in location probability along two orthogonal reference lines830 and 840 within the plot 800.

The plot 800 has bright and dark fringes associated respectively withgreater and lesser probabilities of finding the transmitter 210 incorresponding cells. Graphs 810 and 820 have generally central peaks 850and 860 respectively defining a probability maximum and indicating atransmitter location.

FIG. 9 displays graphs 900 to 908 of standard deviation (sd) in positionestimates as a function of signal to noise ratio for a prior artlocation system of U.S. Pat. No. 5,835,060 and for the present invention(referred to as “SABLE”). The graphs have logarithmic axes, and wereobtained from like computer simulations of the prior art and theinvention. The simulations involved two antennas separated by a distanceL of 4 m, the wavelength was 0.3 m (1 GHz) and the aperture (distancemoved by the system 10) was 10 m, ie±5 m with respect to a centralposition which is broadside on to a transmitter to be located; thetransmitter was at a range of 10 m from the locating system in eachcase, and 1,000 measurements were made, ie one per cm of distance movedby the system 10. At 910 a key is given to the graphs 900 to 908: here“along track” refers to measurement position errors in a dimensionparallel to the location system movement direction, and “range” is theequivalent for errors in a dimension.orthogonal to this generallytowards the transmitter to be located. “Phase” in parenthesis indicatesthat the peak 850/860 in the trajectory azimuth match coefficientMa_(ijk) 800 (transmitter location probability) was obtained bydetermining where the phase of this function went through zero; “Mod” inparenthesis indicates that this peak was obtained by determining theposition of the maximum of the modulus of Ma_(ijk). Graphs 900 and 902show range and along track results for the prior art and graphs 904 to908 those for the present invention.

Graphs 904 and 908 are both standard deviation along track butdetermined from modulus and phase respectively, the latter beingsuperior because it has the lower deviation. Graph 906 is in fact twocoincident graphs superimposed on one another, ie the graphs of standarddeviation in range determined from modulus and phase respectively; thisis indicated by points such as 912 each comprising “x” (Mod) overwrittenby “+” (Phase). The fact that these two graphs are identical indicatesthere is no accuracy advantage in choosing either phase or modulus todetermine location.

The graphs 900 to 908 show that the prior art measurement uncertainty orstandard deviation (sd) is considerably worse (larger) than that of theinvention for all values of signal to noise. Moreover, prior art graphs900 and 902 are actually optimistic, because they level off at a region914 simply because the computer simulation used a finite search volumewhich limited the maximum uncertainty irrespective of signal to noiseratio. Even with this levelling off, the maximum prior art error is over40% whereas that for the invention is 1%. Although these absolute valuesshould be treated with caution because they are simulated, it is correctto infer that the invention exhibits markedly better accuracy (loweruncertainty) than the prior art.

Although the system 10 has been described as incorporating patchantennas for simplicity and cheapness, any other antenna or indeedreceiving waveguide can be used provided signal phase at reception canbe determined from it.

In a dense urban environment a transmitter signal may undergoreflections before reception, and measured phases derived the system 10may be unreliable. This is a well known multipath problem. The system 10should therefore sample radiation from the transmitter 210 frequentlyfrom a variety of different directions in order to collect a largeenough sample of data to resolve uncertainty. Sampling a transmittersignal from many different directions tends to reduce problems withmultipath effects and to improve location reliability.

The system 10 may incorporate inertial navigation sensors such asgyroscopes and accelerometers for monitoring instantaneous orientationand position of the vehicle 20 in combination with a GPS referenceprovided by the base station 160 and the GPS receiver in the navigationunit 50. This provides an advantage that the system 10 can counteractinaccuracies in measured phases differences Δθ_(e,Pq) and Δθ_(a,Pq).

A simplified version of the system 10 would use only two antennas 30, 34and would be largely limited to locating a transmitter in atwo-dimensional field, ie cells C_(ijk) with a single j index value or yaxis position. This requires less computation. However, even with twoantennas, with appropriate platform motion, it is possible to obtainlocation information in all three spatial dimensions.

The system 10 may be adapted to search a larger more remote volume. Itmay be mounted in an aircraft for searching for transmitters in anunderlying scene. Alternatively, it might search a smaller nearby volumesuch as a building. It may also be adapted for operation in sonar byreplacing the antennas 30 to 34 with sonar transducers and arranging forthe transmitter 210 and the signal processing unit 40 to operate at asonar frequency such as 20 kHz. It might be mounted on a satellite forlocating transmitters of unknown origin.

What is claimed is:
 1. A sensor system for transmitter locationincorporating: a) two receiver elements (30, 34) responsive to incidentradiation by generation of respective signals, b) a processing system(40) for determining phase difference data for pairs of element signals,c) means (50) for measuring sensor system position in terms of positiondata; d) computer apparatus (60) for determining transmitter positionfrom phase difference data measured from processed element signals andcalculated from trial transmitter locations, characterised in that thecomputer apparatus (60) is arranged to locate transmitters frommagnitude or phase of circular functions of differentials betweenmeasured and calculated phase difference data.
 2. A sensor systemaccording to claim 1 characterised in that the processing system (40) isarranged to process a pair of element signals or a pair of frequencydownconverted signals equivalent thereto by multiplying one signal ofeach pair in either case by a complex conjugate of the other to enabletheir phase difference to be measured.
 3. A sensor system according toclaim 2 characterised in that the processing system (40) is arranged todetermine phase difference by: a) mixing each signal of a pair with sineand cosine reference signals to determine in-phase and quadraturecomponents, b) multiplying each component of one signal by bothcomponents of the other to produce an in-phase component product, aquadrature component product and two products of in-phase and quadraturecomponents, c) adding the in-phase component product to the quadraturecomponent product, and d) subtracting one product of in-phase andquadrature components from the other.
 4. A sensor system according toclaim 3 characterised in that the processing system (40) is arranged todigitise signals at a sampling rate prior to mixing with referencesignals, the reference signals have a frequency of one quarter of thesampling rate, and mixing is implemented by multiplication of alternatesamples by 0 and one other sample in four by −1.
 5. A sensor systemaccording to claim 1 characterised in that the circular functions arecomplex exponents.
 6. A sensor system according to claim 5 characterisedin that the computer apparatus (60) is arranged to determine actualtransmitter location by summing exponents over a range of systempositions and to indicate transmitter location from the magnitude orphase of this summation.
 7. A sensor system according to claim 5characterised in that the computer apparatus (60) is arranged todetermine actual transmitter location by producing summations ofexponents over a range of system positions, to multiply the summationstogether to form a product and to indicate transmitter location as thatcorresponding to a predetermined magnitude or phase of this product. 8.A sensor system according to claim 1 characterised in that the measuringmeans comprises a GPS base station (160) and co-located with thereceiver elements a GPS subsidiary station (50) for co-operation withthe base station (160) and provision of position data.
 9. A sensorsystem according to claim 8 characterised in that: a) it is movablerelative to a transmitter (210) to be located, b) the base andsubsidiary GPS stations (50, 160) are arranged to provide position data,c) the computer apparatus (60) is arranged to subtract calculated phasedifferences from those of processed element signals for a series ofsensor system positions.
 10. A sensor system according to claim 1characterised in that the measuring means (50) is arranged to implementinertial navigation.
 11. A sensor system according to claim 1characterised in that it incorporates at least three receiver elements(30, 32, 34) disposed to define a plurality of measurement dimensions inwhich to locate a transmitter (210).
 12. A system according to claim 1characterised in that the receiver elements are patch antennas (30, 32,34).
 13. A method of locating a transmitter having the steps of: a)providing two receiver elements (30, 34) responsive to incidentradiation by generation of respective signals, b) determining phasedifference data for pairs of element signals, c) measuring sensor systemposition in terms of position data; d) determining transmitter positionfrom phase difference data measured from processed element signals andcalculated from trial transmitter locations, characterised in thattransmitter position is determined from magnitude or phase of at leastone circular function of a differential between measured and calculatedphase difference data.
 14. A method according to claim 13 characterisedin that determining phase difference data for pairs of element signalsis carried out by multiplying one signal of each pair in either case bya complex conjugate of the other to enable their phase difference to bemeasured.
 15. A method according to claim 14 characterised in thatdetermining phase difference data is carried out by: a) mixing eachsignal of a pair with sine and cosine reference signals to determinein-phase and quadrature components, b) multiplying each component of onesignal by both components of the other to produce an in-phase componentproduct, a quadrature component product and two products of in-phase andquadrature components, c) adding the in-phase component product to thequadrature component product, and d) subtracting one product of in-phaseand quadrature components from the other.
 16. A method according toclaim 15 characterised in that signals are digitised during processingat a sampling rate prior to mixing with reference signals, the referencesignals have a frequency of one quarter of the sampling rate, and mixingis implemented by multiplication of alternate samples by 0 and one othersample in four by −1.
 17. A method according to claim 13 characterisedin that calculated phase differences are produced for a plurality ofpossible transmitter locations and actual transmitter location isdetermined from correlation between calculated and measured phasedifferences.
 18. A method according to claim 13 characterised in thatthe at least one circular function is at least one complex exponent. 19.A method according to claim 18 characterised in that the at least onecomplex exponent is a plurality of complex exponents, actual transmitterlocation is determined by producing a summation of exponents over arange of system positions and indicating transmitter location to be thatcorresponding to a predetermined magnitude or phase of this summation.20. A method according to claim 18 characterised in that the at leastone complex exponent is a plurality of complex exponents, actualtransmitter location is determined by producing a plurality ofsummations of exponents over a range of system positions andcorresponding to respective dimensions of transmitter location,multiplying the summations together to form a product and indicatingtransmitter location to be that corresponding to a predeterminedmagnitude or phase of this product.
 21. A method according to claim 13characterised in that position data is provided by means of a GPS basestation (160) co-operating with a GPS subsidiary station (50) co-locatedwith the receiver elements.
 22. A method according to claim 20characterised in that: a) the receiver elements (30, 32, 34) are movablerelative to a transmitter (210) to be located, b) position data areprovided by base and subsidiary GPS stations (50, 160), c) calculatedphase differences are subtracted from those of processed element signalsfor a series of sensor system positions.
 23. A method according to claim13 characterised in that position data are obtained using inertialnavigation.
 24. A method according to claim 13 characterised in that itemploys at least three receiver elements (30, 32, 34) disposed to definea plurality of measurement dimensions in which to locate a transmitter(210).
 25. A method according to claim 13 characterised in that thereceiver elements (30, 32, 34) are patch antennas.